CALCULATOR-FREE
Question 1
MATHEMATICS METHODS
Find the possible values of $k$, such that $\int_{\frac{\pi}{4}}^k \sin 2t \, dt = -0.5$ where $-\pi \le k \le 2\pi$.
(4 marks)
$\int \sin 2t \, dt$
$\int_{\frac{\pi}{4}}^k \sin 2t \, dt = -0.5$
$= -\frac{1}{2} \cos 2t \, dt$
$\left[ -\frac{1}{2} \cos 2t \right]_{\frac{\pi}{4}}^k = -0.5$
$\left[ -\frac{1}{2} \cos 2t \right]_{\frac{\pi}{4}}^k$
$-\frac{\cos 2k}{2} + \frac{(\cos \frac{\pi}{2})}{2} = -0.5$
